Three formats of a self-supporting card. Because it stands unaided on a surface that gets knocked and wiped, stock weight is structural here rather than cosmetic. Filter by how many sides need to be seen.

Two faces, A-frame. Guests sit opposite one another.

Three faces, rigid base, round tables and bar tops.

Your size, panels or shape: tall, shaped or nonstandard.
Two faces is enough where guests sit opposite one another. Both see a printed side and nothing is wasted. On a round table or a bar, people sit at varying angles and someone always ends up looking at an edge, which is what the three-panel format solves. It is also genuinely more stable, because a triangular base is rigid rather than relying on fold tension.
Whatever the format, print every face. There is no back on a table tent, and a blank side is one that somebody at the table is looking at. Stock is the other half: below about 300gsm a tall tent bows at the fold and tips over, which is the failure everyone has seen on a restaurant table. Lamination adds real stiffness as well as letting the tent be wiped down between services.